354 On the Expenditure of Heat in the Hot-air Engine. 
of air in the ratio, 1:6-°05. If again, we allow an equal expansion 
to steam, the advantage will be. reduced to the ratio 1: 4-40 
Tn all these computations, as in the former article, we have con- 
sidered the value of the co-efficient of capacity for air (or 7) to be 
nly 1:36. ty there can now be no doubt that this ought to be 
put =1-40, or 1-41. Mr. Rankine (Lond. and Ed. Phil. Mag., 
June, 1853) Minis 14094, which is employed in the computa- 
tions that follow. The effe ct of the enlargement of this number, 
is to diminish somewhat the calculated power of the air engine, 
in every case. 
For the sake of making apparent, in a single view, the effect of 
variations in the proportions of the cylinders, and of different posi- 
tions of the cut-off, the following table has been prepared, ex- 
hibiting a large variety of suppositions. The little probability 
which seems now to exist, that any further attempt will be made 
to apply the invention in practice, renders the calculations rather 
curious perhaps than useful ; but they may serve to throw some 
light upon certain questions which have been topics of discussion 
with different writers on this subject. 
In this table, the symbols 7 and mm stand as in the former article, 
for the length of the stroke before the cut-off (the entire stroke 
being unity), and the numerical ratio in cross section between the 
cylinders (that of the working cylinder being unity). In the 
column headed “ heat expended,” are given the numbers of units 
(or degrees F".) which the total theoretic expenditure would be 
capable of imparting to one unit of weight (or pound) of water. 
The column headed R, shows the theoretic ratio of advantage in 
favor of air, as compared with the steam which the heat expended 
would produce at 212°, the steam being supposed to work with- 
out expansion. ‘The column R’, shows a similar ratio, on sup- 
position that the steam expands as much as the air. Since these 
expansions are very variable, the numbers in this column are a 
less eligible criterion by which to judge of the relative theoretic 
economy of air and steam engines, than those of the column R. 
But as steam is often worked with much larger expansion than 
any that air admits of, an additional column is introduced, headed 
R”, which shows the effect of heated air as compared with that 
of the steam generated by the same heat, and expanded to three 
times its original bulk. 
the powers in this table are computed by means of the form- 
ula, p. 248, of the last number of this Journal,* and on the sup- 
* In this formula as there printed there occurs an error. In the last term within 
parenthesis, the factor i” should be SrA 
Also, in the particular formula, top of the following page, the numerator of the 
first fractional term should read jy’(i”"'~1) instead of u/(1’-1). ‘These errors 
are discoverable by following out the steps of the precomes ye precede them, 
